| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 42.0.157...864.1 |
$x^{42} - 2 x^{21} + 2$ |
$42$ |
[0,21] |
$-\,2^{62}\cdot 3^{42}\cdot 7^{42}$ |
$3$ |
$58.4247560083$ |
$88.45533386347503$ |
|
|
✓ |
$D_6\times F_7$ (as 42T95) |
trivial |
$4$ |
$20$ |
$507894019142814700000$ |
| 42.0.330...328.1 |
$x^{42} + 2$ |
$42$ |
[0,21] |
$-\,2^{83}\cdot 3^{42}\cdot 7^{42}$ |
$3$ |
$82.6250823253$ |
$125.09473281396649$ |
|
|
✓ |
$D_6\times F_7$ (as 42T95) |
not computed |
$2$ |
$20$ |
|
| 42.2.330...328.1 |
$x^{42} - 2$ |
$42$ |
[2,20] |
$2^{83}\cdot 3^{42}\cdot 7^{42}$ |
$3$ |
$82.6250823253$ |
$125.09473281396649$ |
|
|
✓ |
$D_6\times F_7$ (as 42T95) |
not computed |
$2$ |
$21$ |
|
| 42.2.155...125.1 |
$x^{42} - 5$ |
$42$ |
[2,20] |
$3^{42}\cdot 5^{41}\cdot 7^{42}$ |
$3$ |
$101.052521836$ |
$152.99395611539884$ |
|
|
|
$D_6\times F_7$ (as 42T95) |
not computed |
$2$ |
$21$ |
|
| 42.0.182...264.1 |
$x^{42} + 9$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 3^{82}\cdot 7^{42}$ |
$3$ |
$119.5777797320877$ |
$154.7452848498471$ |
|
|
? |
$D_6\times F_7$ (as 42T95) |
not computed |
$4$ |
$20$ |
|
| 42.2.547...792.1 |
$x^{42} - 3$ |
$42$ |
[2,20] |
$2^{42}\cdot 3^{83}\cdot 7^{42}$ |
$3$ |
$122.746895057$ |
$154.7452848498471$ |
|
|
✓ |
$D_6\times F_7$ (as 42T95) |
not computed |
$2$ |
$21$ |
|
| 42.0.682...000.1 |
$x^{42} + 5$ |
$42$ |
[0,21] |
$-\,2^{42}\cdot 3^{42}\cdot 5^{41}\cdot 7^{42}$ |
$4$ |
$202.105043673$ |
$305.9879122307977$ |
|
|
✓ |
$D_6\times F_7$ (as 42T95) |
not computed |
$2$ |
$20$ |
|
